In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.

In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum.^[1] A geographic coordinate transformation is a translation among different geodetic datums. Both geographic coordinate conversion and transformation will be considered in this article.

This article assumes readers are already familiar with the content in the articles geographic coordinate system and geodetic datum.

Change of units and format

Informally, specifying a geographic location usually means giving the location's latitude and longitude. The numerical values for latitude and longitude can occur in a number of different units or formats:^[2]

• sexagesimal degree: degrees, minutes, and seconds : 40° 26′ 46″ N 79° 58′ 56″ W
• degrees and decimal minutes: 40° 26.767′ N 79° 58.933′ W
• decimal degrees: +40.446 -79.982

There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula

${\displaystyle {\rm {{decimal\ degrees}={\rm {{degrees}+{\frac {\rm {minutes}}{60}}+{\frac {\rm {seconds}}{3600}}}}}}}$.

To convert back from decimal degree format to degrees minutes seconds format,

${\displaystyle {\begin{aligned}{\rm {absDegrees}}&=|{\rm {{decimal\ degrees}|}}\\{\rm {floorAbsDegrees}}&=\lfloor {\rm {{absDegrees}\rfloor }}\\{\rm {degrees}}&=\operatorname {sgn}({\rm {{decimal\ degrees})\times {\rm {floorAbsDegrees}}}}\\{\rm {minutes}}&=\lfloor 60\times ({\rm {{absDegrees}-{\rm {{floorAbsDegrees})\rfloor }}}}\\{\rm {seconds}}&=3600\times ({\rm {{absDegrees}-{\rm {{floorAbsDegrees})-60\times {\rm {minutes}}}}}}\\\end{aligned}}}$

where ${\displaystyle {\rm {absDegrees}}}$ and ${\displaystyle {\rm {floorAbsDegrees}}}$ are just temporary variables to handle both positive and negative values properly.

Coordinate system conversion

A coordinate system conversion is a conversion from one coordinate system to another, with both coordinate systems based on the same geodetic datum. Common conversion tasks include conversion between geodetic and earth-centered, earth-fixed (ECEF) coordinates and conversion from one type of map projection to another.

From geodetic to ECEF coordinates

Geodetic coordinates (latitude ${\displaystyle \ \phi }$, longitude ${\displaystyle \ \lambda }$, height ${\displaystyle h}$) can be converted into ECEF coordinates using the following equation:^[3]

Zdroj:https://en.wikipedia.org?pojem=Geographic_coordinate_conversion
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